Question: $A$ $B$ $C$ If: $ AC = 87$, $ BC = 2x + 9$, and $ AB = 8x + 8$, Find $BC$.
Answer: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {8x + 8} + {2x + 9} = {87}$ Combine like terms: $ 10x + 17 = {87}$ Subtract $17$ from both sides: $ 10x = 70$ Divide both sides by $10$ to find $x$ $ x = 7$ Substitute $7$ for $x$ in the expression that was given for $BC$ $ BC = 2({7}) + 9$ Simplify: $ {BC = 14 + 9}$ Simplify to find ${BC}$ : $ {BC = 23}$